Apparent horizons, black hole entropy, and loop quantum gravity

In recent work on black hole entropy in nonperturbutive quantum gravity, an action for the black hole sector of the phase space was introduced and (partially) quantized. We give a number of observations on this and related works. In particular we show that (i) the entropy calculation applies without change to generally covariant theories having no black hole solutions, (ii) the phase space constraint used to select the black hole sector is not the apparent horizon equation, which is the natural phase space constraint separating trapped and untrapped regions on an initial data surface, and (iii) there appears to he at least one other phase space constraint which leads to the conclusion that the entropy associated with a hounding two-dimensional surface is proportional to its area. [S0556-2821(99)00208-8].